persepsi1ea

2022-02-15

Confusion about properties of linear transformation.
I learned from 3Blue1Brown's Linear Algebra videos that one of the rules for a transformation to be linear is that the origin remains fixed in place after transformation. So if $T\left(x\right)=x+a$ is a given transformation, I know that by inserting $x=0$, it is not a linear transformation. I am not able to understand what is non-linear about it.

Layla Humphrey

Because $T\left(0+0\right)=a$, whereas $T\left(0\right)+T\left(0\right)=2a$, which is different from a (unless $a=0$, of course). But one should have $T\left(0+0\right)=T\left(0\right)+T\left(0\right)$ if T was linear.

monogamab0f